Earlier quoted context omitted.
I remember meeting NVIDIA in the late aughts (2007?) first launching their CUDA efforts. Really the product was a re-branded 780GTX or whatever their high end gaming card was at the time more or less, but they already laid out a clear pathway to today (more or less).
I remember meeting with them in the mid aughts when they were first talking to HPC folks about using their cards for science. I'll never forget what the chief scientist from nVidia said. "What is the color of a NaN? That is, when you render a texture with a nan value, what does it look like? I'll tell: it's nvidia green."
Where both the sign (s) and the x bits can be anything and it will still be treated as a NaN.
There are lots of ways to encode colour, but there would be too much red with RGBA, and ARGB could be almost any opaque colour, but the red channel has to be at least 0x80, which is still too much red.
So NaNs are too red to encode nvidia green.